If A=B, then AnB=AuB

- anonymous

If A=B, then AnB=AuB

- Stacey Warren - Expert brainly.com

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- chestercat

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- DebbieG

ok... and? :)

- DebbieG

Welcome to Open Study, by the way! :)
What's the question? are you supposed to prove this?

- anonymous

That it does always, never, or sometimes?

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- DebbieG

Ah, ok... well, what do you think?

- DebbieG

It's kind of hard to Venn diagram it, since A=B are just the same circle, right?
so if A=B then everything that's in A is in B, and everything that's in B is in A (there is no difference between the 2, no elements in 1 that aren't in the other).
so what does that mean for the union?
What does that mean for the intersection?

- anonymous

Not sure. Isn't that if A=B then AnB=B and AuB=B, so is it never?

- DebbieG

welll.....
But the question is:
Does A=B imply that AnB=AuB?
You just said that A=B implies that AnB=B and AuB=B... which I'll agree with.....
So, DOES it mean that AnB=AuB?

- DebbieG

By the way, A=B also implies that AnB=A and AuB=A.
Remember, they are the SAME sets.

- anonymous

So it is always?

- DebbieG

Think about what it MEANS, that A=B.... don't just try to "fit" this into some rule you've already learned.
A=B means they have EXACTLY the same elements.
So what's in A{intersect}B ?? Everything that is BOTH sets, right?
What in A{union}B ?? Everything that is in EITHER set, right?
Well, THEY ARE THE SAME SETS. So, isn't everything that's in BOTH, also in EITHER?

- DebbieG

Yes, I would think always. Because they are the same sets, so every element that is in EITHER set, it in BOTH sets.
And every element in BOTH sets is in EITHER set.
They are the same. :)

- anonymous

I know intersections are the same numbers that they have in common and and union is of all the numbers combined but not repeated.

- DebbieG

Try a few examples to convince yourself... that doesn't PROVE it, but it will help you gain intuition.
A={1,3,5,7,8}, .B={1,3,5,7,8}
What's the union? what's the intersection?
See what I mean? :)

- anonymous

The union is {1,3,5,7,8} and so if the intersection. Right?

- anonymous

*is

- DebbieG

Right...
|dw:1378686614862:dw|
Now, imagine that picture if A=B... the circles "slide" over so that they are exactly on top of each other (the sets are the same).
Think about what happens to the intersection area, and the union area. BOTH just become identical to the circle.

- DebbieG

And yes, that's right. Like I said, doesn't PROVE that it's "always" but helps you get some intuition around it.

- anonymous

Can you help me with evaluate the expression 5^-1/5^0?

- DebbieG

I will, but in the future please post each question separately, not in the same thread. It just works better. :)
So is the expression
\(\Large \dfrac{5^{-1}}{5^0}\) ?

- DebbieG

You just need a couple of rules for exponents. Actually, there are a couple of ways to go about this one... but you will need:
\(\Large a^{-1}=\dfrac{1}{a}\)

- anonymous

Ok. Yes.

- DebbieG

And also \(a^0=1\) for any base, a. Does that sound familiar?

- DebbieG

So apply those two rules to your expression: \(\Large \dfrac{5^{-1}}{5^0}\)
OR, alternatively, you COULD just use this rule:
\(\Large \dfrac{a^{m}}{a^n}=a^{m-n}\)

- anonymous

Yes.

- DebbieG

OK, you should have everything you need there to simplify the expression. Go ahead and try.

- anonymous

I can't remember how to begin. I'm trying to help my daughter who is on homebound due to surgery.

- anonymous

It has been years since I have had Algebra.

- anonymous

I have that it is 1/5 / 1

- DebbieG

that's a bit hard to interpret... lol.. but I think you have it, if you mean:
\[\Large \dfrac{ \dfrac{ 1 }{ 5 } }{ 1 }\]
but notice that you can "simplify" it, since there is no need to write anything over the den'r of 1. That is, a/1 = 1.
so you just write:
\(\Large \dfrac{ 1 }{ 5 } \) :)

- DebbieG

Also, you get that simply if you use the rule I gave above:
\(\Large \dfrac{a^{m}}{a^n}=a^{m-n}\)
Then you have:
\(\Large \dfrac{5^{-1}}{5^0}=5^{-1-0}=5^{-1}= \dfrac{1}{5}\)

- anonymous

Thank you so much :) It is hard to teach a child Algebra when you have been out of school for so long and have forgotten everything yourself and are having to relearn yourself.

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